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MỤC LỤC
BỘ GIÁO DỤC VÀ ĐÀO TẠO 9
BỘ GIÁO DỤC VÀ ĐÀO TẠO 9
TÌM HIỂU BÀI TOÁN NHẬN DẠNG BIỂN SỐ XE 10
ĐỒ ÁN TỐT NGHIỆP ĐẠI HỌC HỆ CHÍNH QUY 10

Ngành: Công nghệ thông tin 10
BỘ GIÁO DỤC VÀ ĐÀO TẠO 10
TÌM HIỂU BÀI TOÁN NHẬN DẠNG BIỂN SỐ XE 10
PHẦN GIỚI THIỆU 13
Chương 1: 14
TỔNG QUAN VỀ BÀI TOÁN NHẬN DẠNG BIẾN SỐ XE 14
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Chương 2: 24
PHÁT HIỆN VÙNG CHỨA BIỂN SỐ XE 24
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Chương 3: 40
BÀI TOÁN NHẬN DẠNG KÝ TỰ 40
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TÀI LIỆU THAM KHẢO 62
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1.2. Khái niệm về nhận dạng biển số xe:
1.2.1 Khái niệm & ứng dụng:
a) Khái niệm:
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Q)*2(M<5d8)*T/U)GH.a3)MVu.*,)'K:92/@V=u.*/_.T8'*/*v)*2(*v)*Q)*B
19:5b)'O(M<5d8)*5<5.*,)'./))*>+5*xG•*€:MVu.*V=@•/MV2?/.H5d]
5*S7uBBBB
*) Phân loi ứng dụng nhận dng biển số xe:
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Q)*2(M<5d8)*T/U)GHMV.•5<5*v)*Q)*5*Y`d>t5.•5<5.*/_.T8.*:*v)*B
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./_`.*:)*S).•597Va9Ba=)'T<=5<=.H.)'*/-`5x9V75*‘@•)'O6/•7X5
M<5d8)*d>t5T/U)GHMV|M<5d8)*5<55*€}.•5<5TX5Q)*B
l)*/L:5<5*.*X5f*<5)*9:dU`*Z)O=6/5<5X)'@Y)')*S)@6)'T/U)
GHMVBE]..a=)')*€)'5<5*dg)'/Q)O(`*Z)O=6/X)'@Y)')*S)@6)'T/U)GH

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5,)'2/-5dq:./3)O(@c.v7.a=)'Q)*udUM<5d8)*dz)'2b)')(=O(T/U)GHMVB
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5<=)(^u5*‘)3:5<5*.*X5'/Q/K:^_.O(O(7G9=)*S)@6)'|On5a9}d>t55<5fP
.4GH2(5*€B
b)Ứng dụng của hệ thống nhận dng biển số xe:
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f/U7G=<.5<5`*>g)'./-)B>?/dZ^5*z)'.9dL5S`d_)7].GHX)'@Y)'`*e
T/_)dH/2?/*-.*H)')*S)@6)'T/U)GHMV+
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•}J/U7G=<.MV.6/5<5d>‚)'T/3)'/?/+E•/K:H5'/9dL:5l)*€)'K:^
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1.2.2 Phân loại biển số xe:
Trước tiên là quy định biển số của 64 tỉnh thành (Biển trắng chữ đen):
00Ž9={)'
0 Ž6)'1g)
0RŽ$:Q)'/)*

0Iu0iŽQ/*c)'
0[Ž*</v)*
0kŽ978)*
0"Ž*z*n
!Ž*</':^3)
0Ž&3)</
Ž:^3)$:9)'
\Ž(/9)'
RŽ(=9/
IŽ9/*Z:
iŽ1g)9
[Ž/-)/3)
kŽc9v)*
"u\!u\0u\ Ž(]/
\\Ž(Z^
\RŽQ/>g)'
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™}Những quy định về màu sắc và chữ số đặc biệt:
1. Màu xanh chữ trắng là biển xe của các cơ quan hành chính sự nghiệp:
Ža45.*:]55*m)*`*x.*vO(T/U)M9)*k!
0[
Ž<5.‘)*.*()*.*v.*V=GH.>g)'X)'
2. Màu đỏ chữ trắng là biển xe trong quân đội:
—+/)*d=()0 
—+$:Z)=()Ru/)*d=()5N:O=)'
+T]T/)*
+/)*5*x)',)'/)*
+/)*5*x)'*=<*n5
1+/)*d=()a>‚)'1g)
+/)*5*x)'.*,)'./)O/3)O65
+].>O-)*T/3)`*c)'
+n52/-)OY5K:Z)
+n52/-)K:Z)^
J—+$:Z)f*:0
J+$:Z)f*: 
J+$:Z)f*:\
J+$:Z)f*:R
J+$:Z)f*:I
J+$:Z)f*:[
JJ+$:Z)f*:"
+<5K:Z)^2/-)
$+$:Z)5*x)'*Q/K:Z)
$Ju$+$:Z)5*x)'`*c)'f*,)'f*,)'K:Z)

+e)'5Y55*m)*.a8
+e)'5Y5*S:5q)
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+e)'5Y5fj.*:S.
E+].e)'.*977>:
+/V VO
3. Màu trắng 2 chữ, 5 số là biển dành cho người nước ngoài:
ŽO(MV)'=6/'/9=
0k
ŽO(MV5x95<5.e5*X5u5<)*Z))>?5)'=(/+a=)'dl\GH•'/€9O(
7FK:H5'/9u GH./_`.*V=O(GH.*X.4B
™pVGHk!MMMŽ^^O(T/U)5w`5*=5<5d6/GXK:<)u.*37'65*dš•
'/€92( GH5:H/O(!0O(T/U)MV5x9.e)'OF)*G4
4. Những xe mang biển 80 gồm có :
Ž<59)5x9a:)'>g)'Q)'
Žy)`*c)'*x.85*)>?5
Žy)`*c)'$:H5*]/
Žy)`*c)'*m)*`*x
Ž],)'9)
ŽpV`*Y52Y5<5d‹)'5*m:;2/3)a:)'>g)'Q)'5,)'.<5.6/(]/
2(5<5.*()*2/3)*m)*`*x
Ž])'=6/'/9=
Ž/-)f/U7G=<.)*Z)@Z).H/59=
Ž=(<))*Z)@Z).H/59=
Ž(/.a:^L)*v)*/ 97
Ž(/./_)')l// 97
Ž*,)'.w)MF/ 97
Ž<=)*Z)@Z)
Ž*9)*.a9*()>?5
Žn52/-)*m)*.a8K:H5'/9

Ž9)K:Q)OPy)'uQ=.()'uf*:/.m5*O85*GN‹*mE/)*›
Ža:)'.Z7O>:.a€K:H5'/9
Ž%;T9)Z)GHf_*=65**=<'/9dv)*
Že)'5,)'.^q:f*m/ 97
Ž<5d6/GXK:<)u.e5*X5K:H5._2()*Z)2/3))'>‚/)>?5)'=(/
Ž%;T9)*X)'f*=<)*()>?5
ŽY5()'f*,)'@Z)@Y)'/ 97
ŽJ/U7.=<))*()>?5
0"
5. Các biển A+
pV5x9,)'—)ŽQ)*1<..>g)'X)'2?/5<5.‘)*
2m@Y+\0—œMV5x9,)'—)ŽQ)*1<..*()*`*H(]/
1.3. Một số hướng giải quyết bài toán nhận dạng biển số xe:
law.)*/L:`*>g)'`*<`./_`5S)Ba=)'dl5l*9/5<5*./_`5S)`*eT/_)
@>?/dZ^+
1.3.1. Hướng tiếp cận phát triển vùng:
• *l7.<5'/Q/'VO˜*^.V9)@—@a/V)J/Va)9)d>t5d6/@/-)5*=5<5*
./_` 
5S))(^
• •.>•)'5x9`*>g)'`*<`)(^+dlO(T/U)GHMV.*>‚)'5*X97].7(:
d‹)')*w.u5*o)'*6)7(:.aŒ)'u2(5l@/-).m5*.>g)'dH/)*w.d8)*Bv2S^5l
.*U@b)'`*>g)'`*<``*<..a/U)2b)'u*=~5GN@Y)'f*:)'5*€)*S.@/5*:^U)
.a=)'dU.v7a92b)'5l.m)*5*w..*š97F)T/U)GHMV2(./_)*()*)*S)@6)'B
• :d/U7+aw.dg)'/Q)u2(MNOPaw.)*9)*dH/2?/)*€)'Q)*5*‘5*X9
2b)'T/U)GHMVB
• *>t5d/U7+f*/Q)*5l.*37)*/L:dH/.>t)'f*,)'`*Q/O(2b)'T/U)
GHMVu5*o)'*6)O(Q)*5*Y`.e)'K:<.'‹75Q5Q)*2S.T3))'=(/.*v5<5*./_`
5S))(^.a•)3)f*,)'*/-:K:QBv2S^`*>g)'`*<`)(^aw.*/-:K:QdH/2?/*-
.*H)'.a67.*:`*mu.a67'<55e)'u'N/MV.4d])'
1.3.2. Hướng tiếp cận dò biên và biến đổi Hough:

• *l7.<5'/QE/5*9VO/@V)T9:7u=GV)—OVM9)@Vau/5*/f1Va'V^u
19)@OVa=79)d>t5d6/@/-)5*=5<5*./_`5S))(^B
• •.>•)'5x95<5*./_`5S))(^O(+/U)GHMVd>t5T9=T=5T•/d>‚)'
2/L)B=dlu5l.*U@b)'`*>g)'`*<``*<.*/-)T/3)uG9:dl@b)'`*’`T/_)de/
=:'*dU.am5*)*€)'d=6).*o)'@n5u)'9)'.‹).6/.a=)'Q)*B/9=d/U75x9
)*€)'d=6).*o)')(^5*m)*O(2b)'T9=5*X9T/U)GHMVB(5:H/5b)'O(./_)
*()*)*S)@6)'5<5fP.4•.a3)7•/2b)'5=)B
• :d/U7+d]5*m)*M<559=B(5<5*-.*H)')*S)@6)'d9`*q)dL:
`*<..a/U).*V=*>?)'./_`5S))(^B
!
• *>t5d/U7+]`*X5.6`.m)*.=<)f*<59=BJ*/Q)*5l.*37)*/3:
dH/.>t)'f*<5.*vf*H/O>t)'.m)*.=<).y)'O3)aw.)*/L:B=7Y5dm5*O(`*Q/
M<5d8)*d>t52b)'5=))(=5*X9T/U)GHMVB
'=(/*9/5<5*./_`5S).a3)u5c)5l)*/L:5<5*./_`5S)f*<5dUM<5d8)*
5*m)*M<52b)')(=5*X9T/U)GHMV2(T>?55:H/5b)'O(./_)*()*)*S)@6)'
fP.4BE•/5<5*./_`5S)5l7].>:2()*>t5d/U7B9GH5<5X)'@Y)'dL:GN
@Y)'5<5*./_`5S)T/_)de/=:'*Ba=)'T<=5<=dL.(/5x9V7uV7M/).av)*T(^
5<5*./_`5S)=:'*B
1.4 Hướng giải quyết:
ž`*q)0B\5*z)'.9dF.v7*/U: *>?)''/Q/K:^_.5*=2/-5M<5d/)*
2b)'5*X9T/U)GHMVBE•/5<5*'/Q/K:^_.5l)*€)'>:d/U72(*6)5*_a/3)'
5x9)lB
*) Một số đặc điểm về biển số xe ở Việt Nam:
• /3:5*:Ÿ)2Lfm5*.*>?5+ž7•/)>?5.*>‚)'5l./3:5*:Ÿ)2Lfm5*
.*>?5)*w.d8)*BH/2?/)>?5.9uT/U)GHMVK:/d8)*f*<d‹)'dL:5*=7•/O=6/
MVu.;O-5*/L:@(/ua])'5*=7•/O=6/MVO()*>)*9:BH/2?/O=6/MV5l7].
*()'fP.4.*v.‘O-@(/ra])'O(+
IBRrIB\
≤≤
HW

BH/2?/O=6/MV5l*9/*()'fP
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RB0rkB! ≤≤ HW
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5*/L:59=5x97•/fP.4O:,))*š*g)kI 5*/L:59=5x9T/U)GHMV2(O:,)O?)
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5*/L:@(/5x9T/U)GHMVBE•/fP.45x9T/U)GHMVd>t5MV7)*>O(7].2b)'
O/3).*,)'5=)B=dlu5*z)'.95l.*Ud_72b)'O/3).*,)'5=).*š97F).m)*
5*w.dlO(fP.4B*zPGHfP.4.a3)T/U)GHMVO(.•id_)0!fP.4Bž)>?5.9
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I
B{)'5<5*<`
@Y)'`*>g)'`*<`2(fj.*:S.)*S)@6)'fP.4
$:9T9T>?5)*>.a3).95l.*U)*S)@6)'d>t5T/U)GHMV
£
c
I
Ba=)'T>?5
\+)*S)@6)'fP.4V7GN@Y)'`*>g)'`*<`76)')=a=).a:^L))'>t55*=2/-5
)*S)@6)'fP.4B

a=)'`*q)./_`.*V=dlO(5*/./_..•)'T>?5MNOPT(/.=<))*S)@6)'
T/U)GHMVu2(7].GHf*</)/-75gTQ)K:V).*:]57(5lO/3)K:9)d_))*S)
@6)'T/U)GHMVB
\
Chương 2:
PHÁT HIỆN VÙNG CHỨA BIỂN SỐ XE
2.1 Một số khái niệm cơ bản:
2.1.1 Tổng quan về ảnh
a. Ảnh và điểm ảnh:
)*O(7Q)'GH.*45*9/5*/L:

( )
nm
I
u
u5lfm5*.*>?5|EM}u.a=)'dl7•/
'/<.a8
( )
nm
I
u
|.6/7].d/U7Q)*}uT/U:.*87X5M<75x9Q)*.6/28.am
( )
nmu
.>g)'
X)'
E].Q)*O(Q)*)*8`*Z))_:'/<.a8
( )
nm
I
u
T{)'!*=~50B
b. Mức xám:
EX5M<7O(f_.K:QG47F*l9.>g)'X)'7].5>‚)'d]G9)'5x97•/
d/U7Q)*2?/7].'/<.a8GHŽf_.K:Q5x9K:<.av)*O>t)'*l9B<5*7F*l9f/)*
d/U).*>‚)'@b)'0iu\ uiRBEF*l9 Ii7X5O(`*e@Y)')*w.@=OP@=fj
.*:S.Bv
k
œ Iiu)3)2?/ Ii7X5u7•/`/MVOd>t57F*l9kT/.B
c. Đối tượng ảnh:
a=)'`*q))(^.95*‘M’.2?/Q)*)*8`*Z)u2v7n/Q)*)*8`*Z)dL:5l

.*Ud>92LQ)*)*8`*Z)T{)'5<5fj.*:S.`*Z))'>h)'B9fP*/-:ŠO(.S`5<5
d/U72b)'|d/U7dV)}2(
E
O(.S`5<5d/U7)L)|d/U7.aŒ)'}B9/d/U7
G
2(
V
∈

( )
nm
I
u
){7.a=)'Š|*=~5
E
}d>t5'n/O(RO/3).*,)'|kO/3).*,)'})_:.‹).6/
7].@F^5<5d/U7'n/O(d>‚)'d/+
•
( )
!!
u ji
œ
G
2(
( )
nn
ji u
œ
V
•

( )
!!
u ji
( )
00
u ji→
→
„B
( )
nn
ji u→
7(
( )
Eji
kk
∈u
2?/7n/fœ!u0„u)
•
( )
kk
ji u
O(RO<)''/_)'|kO<)''/_)'}5x9 
( )
00
u
−− kk
ji
 2?/7n/fœ0u u
„u)
d. 4- Láng giềng và 8- láng giềng:

_:
( )
nmu
O(7].d/U7Q)*u.*vRO<)''/L)'5x9)lO(5<5d/U7•)'9^
T3).a3)u@>?/u`*Q/u2(.a</B9fP*/-:
R
N
O(.S`RO<)''/L)'5x9d/U7
( )
nmu
B
⇒
R
N
( ) ( ) ( ) ( ){ }
0uu0uuu0uu0 +−+−= nmnmnmnm
>g)'.4.95l.S`kŽO<)''/L)'
k
N
R
⇒
k
N
( ) ( ) ( ) ( ){ }
0u0u0u0u0u0u0u0
R
+−−+−−++∪= nmnmnmnmN
e. Chu tuyến của ảnh:
Định nghĩa chu tuyến:
*:.:^_)5x97].dH/.>t)'Q)*

( )
nm
I
u
O(@F^5<5d/U75x9dH/.>t)'+
n
ppp →→→ BBBB
0!
B19=5*=
0−i
p
u
0+i
p
O(kO<)''/L)'5x9
i
p
u
Ip ∉∃
£
2(`
¤
O(R
O<)''/L)'5x9`
/
u2(
n
pp ≡
!
BJ*/dl.9'n/)O(d]@(/*9^5*:2/5x95*:.:^_)B

Chu tuyến đối ngầu:
9/5*:.:^_)œ¥0u u„u)¦2(¤œ¥$0u$ u„u$)¦d>t5'n/O(
*9/5*:.:^_)dH/)'A:5x9)*9:)_:2(5*‘)_:+
•
ji∃∀
G9=5*=/2($§O(kO<)''/L)'5x9)*9:
• <5d/U7/O(Q)*.*v$§O()L)2()'>t5O6/B
Chu tuyến trong:
*:.:^_)d>t5'n/O(5*:.:^_).a=)')_:2(5*‘)_:+
• *:.:^_)dH/)'A:¤5x9)lO(5*:.:^_)5x95<5d/U7)_)B
• ]@(/5x95*:.:^_)¤)*š*g)d]@(/5x95*:.:^_)
Chu tuyến ngoài:
*:.:^_)d>t5'n/O(5*:.:^_))'=(/)_:2(5*‘)_:+
• *:.:^_)dH/)'A:¤5x9O(5*:.:^_)5<5d/U7)L)
• ]@(/5x95*:.:^_)¤O?)*g)d]@(/5x95*:.:^_)
•d8)*)'*†9u.9.*w^5*:.:^_))'=(/5x97].dH/.>t)'O(7].d9'/<5
5ld]@(^T{)'7].T9=K:9)*dH/.>t)'B
2.1.2 Phương pháp tách dò ngưỡng tự động
( )
gh
+O(.e)'GH7X5M<7'
n/+
( ) ( )
∑
≤
=
gi
ihgt
a=)'dl+ ”1Hd/U7Q)*d>t5M’.œ7™)
”1H7X5M<7d>t5M’.

n/
( )
( )
( )
( )
∑
∑
=
=
=






=
g
i
g
i
iiP
gt
iih
gm
!
!
O('/<.a8.a:)'Tv)*5w`M<7'
I
( )

( )
( )
( ) ( )
[ ]
00

−−−∗
−
= Gmgm
gtP
gt
gf
( )
gf79M9a'=
θ
2?/
0Ž'! <<
S^G:^a9
θ
O()'>h)'5x9Q)*
2.2 Biên và các phương pháp phát hiện biên.
*) Khái niệm về biên:
/3)O(7].2w)dL5*x^_:.a=)'`*Z).m5*Q)*2v5<5fj.*:S.`*Z)d=6)
Q)*5*x^_:@492(=T/3)BE].d/U7Q)*5l.*U5=/O(d/U7T/3))_:5lG4.*9^
de/d].)'].2(7X5M<7*9^T/3)O(d/U75l5w`M<75l'/<.a8f*<5*o)5<5
d/U7M:)'K:9)*BS`*t`5<5d/U7T/3).6=.*()*T/3)*9^d>‚)'T9=5x9Q)*
*) Các phương pháp phát hiện biên:
*) Phương pháp tiếp cận theo kiểu cổ điển
Z^O(`*>g)'`*<`@492(=G4T/_).*/3)2L'/<.a8d]G9)'5x9d/U7
Q)*BJj.*:S.5*x^_:@b)'`*<.*/-)T/3)•dZ^O(fj.*:S.d6=*(7B_:Ow^

d6=*(7TS5)*w.5x9Q)*.95l`*>g)'`*<`a9@/V).u)_:Ow^d6=*(7TS5*9/
.95=fj.*:S.9`O95VB9/`*>g)'`*<`.a3)d>t5'n/O(`*>g)'`*<`@cT/3)
5Y5T]B
2.2.1 Phương pháp gradient
492(=545d6/*l95x9d6=*(7B*V=d8)*)'*†9u'a9@/V).O(7].2V5.=
5l5<5.*()*`*q)T/U:.*8.H5d].*9^de/'/<.a85x9d/U7Q)*.*V= *>?)'M2(
^B<5.*()*`*q)5x9a9@/V).d>t5.m)*T•/+
dx
yxfydxxf
fx
x
yxf }u|}u|}u| −+
≈=
∂
∂
dy
yxfdyyxf
fx
y
yxf }u|}u|}u| −+
≈=
∂
∂
e/G9)'.n9d]545
θ
a5=GM
=
θ
G/)ry =
1:^a9+

θθ
G/)5=G
y
f
x
f
r
f
∂
∂
+
∂
∂
=
∂
∂
i
θθ
5=G}G/)|
y
f
r
x
f
r
f
∂
∂
+−
∂

∂
=
∂
∂
?/@MO(f*=Q)'5<5*'/€95<5d/U7.*V=*>?)'M|f*=Q)'5<5*.m)*
T{)'GHd/U7}2(.>g)'.42?/@^Ba3).*45._)'>‚/.9*9^@b)'2?/@Mœ@^œ0
?/7].Q)*O/3).Y5¨|Mu^}u5<5d6=*(7a/3)'5x9)l5*=`*’`M<5d8)*
28.am5Y5T].*V=*>?)'5x9T/3)B*452S^u'a9@/V).5x97].Q)*O/3).Y5ud>t5
T/U:@/s)T•/7].*(7¨|Mu^}u@n5.*V=a2?/'l5
θ
ud>t5d8)*)'*†9T•/+
dr
dy
y
f
dr
dx
x
f
dr
df
∂
∂
+
∂
∂
=
œ¨
M
5=G

θ
•¨
^
G/)
θ
*zP+f*/.9)l/Ow^d6=*(75x9Q)*)*>)'.*45a95*‘O(7,`*š)'2(
Mw`M‘d6=*(7T{)'5<5fj.*:S.)*Z)5*S`|`*’`5:])}B=Q)*GHO(.m)*/-:
a‚/a65)3)d6=*(7f*,)'.‹).6/
Jj.*:S.a9@/V).GN@Y)'7].5~`7~.)6
0
 2(

 .a45'/9=|.*V=
*>?)'2:,)''l5}B_:d8)*)'*†9'
0
u'

O('a9@/V)..>g)'X)'.*V= *>?)'M
2(^u.*vT/3)d]5x9'a9@/V).ufP*/-:O('.6/d/U7|7u)}d>t5.m)*.*V=5,)'
.*X5+
—
!
œ'|7u)}œ
}u|}u|



0
nmgnmg +
|0}

}}u|r}u||.9)}u|
0
0
nmgnmgnm
−
=
θ
| }
*zP+dU'/Q7.m)*.=<)u5,)'.*X5|0}d>t5.m)*'q)dz)'T•/+
}u|}u|
0!
nmgnmgA +=
<5.=<).Nd6=*(7d>t5<`@Y)'O(f*<)*/L:u•dZ^u.95*‘M’.7].GH
.=<).N./3:T/U:+.=<).N=TVa.u1=OTVO„
*)Kỹ thuật Robert
?/7•/d/U7Q)*|Mu^}5x9ud6=*(7.*V=Mu .*V=^d>t5fP*/-:
.>g)'X)'T•/'
M
u'
^
d>t5.m)*+






−+=
−+=
}u|}0u|

}u|}u0|
yxIyxIg
yxIyxIg
y
x
/L:)(^.>g)'d>g)'2?/2/-55*S`Q)*2?/ 7~.)6
0
2(

+






=
!0
0!
0
H







−
−

=
0!
!0

H
[
$:<.av)*.m)*.=<)d>t5.*45*/-)K:95<5T>?5G9:+
• >?50+m)*
xx
HII ⊗=
2(
yy
HII ⊗=
• >?5 +m)*

yx
II +
•79.aS)

yx
II +
5*n)a95<5d/U759=.*X u*=~5.*X\BB5*/_7d9GH
*)Kỹ thuật PreWitt:
Jj.*:S.)(^GN@Y)'*9/7~.)6
0
2(

+
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

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−
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$:<.av)*.m)*.=<)d>t5.*45*/-)K:9 T>?5+
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y
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• >?5 +m)*
x
HI ⊗
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y
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>g)'.4)*>fj.*:S.aV˜/ ufj.*:S.1=TVOGN@Y)' 79.aS)7~.)6
)*Z)5*S`O(+
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2.2.2. Kỹ thuật Laplace:
<5`*>g)'`*<`d<)*'/<a9@/V).•.a3)O(72/-5f*<.H.f*/7(d]
G9)'.*9^de/a•)’.BJ*/7X5M<7|'/<.a8.6/7].d/U75x9Q)*}.*9^de/5*S7u
7/L)5*:^U)./_`.aQ/a])'u.*v.95l`*>g)'`*<`9`O95V|d6=*(7TS5*9/}5l

*/-:K:Q*g)B=<).N9`O95Vd>t5d8)*)'*†9)*>G9:+





dy
f
dx
f
f
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+
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=∇
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( ) ( )( )
( ) ( )
[ ]
( ) ( )
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yxfyxfyxfyxf
x
yxfyxf
x
f
x
x
f
u0uuu0

uu0


−−−−+≈
∇
−+∇
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
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k
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( ) ( ) ( )
0uu 0u


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∇
yxfyxfyxf
y
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*(7TS5 B>?/dZ^O(\f/U:7~.)6*9^@b)'+
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•|M•0u^•0}Ž|Mu^•0}
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x
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y
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I

−∇=
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2.3 Phát hiện vùng chứa biển số xe
1gd‹5<5T>?5d>t57,.Q.a=)'*v)*@>?/
)*dq:2(=+O(7].Q)*5l Ii7X5M<7ud>t5)*8`*Z)*l9.*()*Q)*
)*8`*Z)BEY5dm5*5x9'/9/d=6))*8`*Z)*l9Q)*O()*{7O(7)e/TS.2b)'
T/U)GHMVBJ*/.9.<5*T/3)u2b)'T9=5x9T/U)GHMVGƒ*/-)O3)a•a()'B19:dl
@b)'`*>g)'`*<``*<.*/-)T/3)dU5ld>t5T/3)@n52(=)'9)'5x9Q)*BJ_.
K:Q5x95,)'d=6))(^uQ)*.*:d>t5O(Q)*)*8`*Z)5*‘5*X95<556)*@n52(
)'9)'B*45*/-)T/_)de/=:'*5*=5<5d=6)T/3)2•9Ow^d>t52(M<5d8)*
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5
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2.3.1. Nhị phân hóa ảnh
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M<7.*v2/-5`*<.*/-)T/3)f*,)'*/-:K:Qu2vG4.*9^de/O/3).Y55x95<57X5
M<7O(75*=2/-5M<5d8)*T/3)f*,)'`*Q/@s@()'u2(2/-5.v7a95<52b)'O/3)
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5
Hình 2.1: Sơ đồ giải quyết
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rrq:a9O(Q)*)*8`*Z)
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¨=a|/)./œ!›/¥7›/••}
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|T=:)@9a^}B<5d>‚)'T/3)5l.*Ud>t5MV7O(5<556)*@n52()'9)'BEY5
dm5*5x9'/9/d=6))(^O(.<5*a95<556)*@n52()'9)'dU.v7a92b)'5=)5*X9
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Q)*)*8`*Z)u)3).*m5**t`2?/`*>g)'`*<`d6=*(7TS5)*w.Bb)'*9/79
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⇒
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Hình 2.2 Trục tọa độ đề các đi qua 2 điểm
Hình 2.3. Trục tọa độ đề các